Not necessarily, tweak it to run slightly fast and rely on the natural dampening ability of a magnetic field to generate a slowing force on moving conductors, then apply a (an extremely) modest (AC to demagnetize) and controlled magnetic field to slow it down to dead on accurate (probably as determined by a $10 GPS module, or I guess a 7 or so pound gps module). Also you can sense pendulum position with the usual optical technologies, so no contact with historical relics needed there either.
Given the "fun" of controlling precision currents vs the ease of controlling precision times/durations its probably easier to run a standardized constant current thru the correctional electromagnet for a varying X nanoseconds just before the top of the hour rather than trying for a continuous 8 bit precision field that'll never really settle down.
A better design than running the correction routine hourly would be continuous position/time monitoring and run the correction field every time the phase variance between the clock and a GPS receiver exceeds a tenth of a second absolute difference or whatever, then monitor how often that correction happens (and alert when broken, etc).
The best part of doing it non-contact is other than dust not settling where the apparatus is sitting, hundreds of years from now researcher types will have no evidence the apparatus was there. Which I guess would be good if they're researching 1800s clocks and bad if they're researching 2000s microcontrollers... hmm.
I am also thinking of unfortunate scenario where someone adds /removes momentum accidentally while trying to place pennies.
I invite an armchair physics teacher to explain why this is different. Probably something to do with shifting the center of mass closer to the axle.
The article repeatedly says they add weights to the pendulum though, which makes me wonder whether either (a) it's some connected mechanism they add weights to, or (b) this is somewhere reality diverges from the simple model.
They're added directly to the 'pendulum shelf' which looks like it's right at the top of the pendulum. That would adjust the length up (shorter) by a tiny amount by shifting the center of mass of the pendulum up. This squares with the simple model of a pendulum.
For such a famous clock you would think they'd create some kind of perfectly accurate weight, but I guess this gives them more control (Easier to add and remove weight, and why make custom weights when you have a few in your pocket?!)
British engineering at its finest. I understand they have a stock of discontinued six-pences and ha'pennies which weigh only a few grammes each and are used for these fine adjustments.